A Taxonomy of Gnoses

Anyone who was studied a difficult technical subject like mathematics has surely had the following experience:

You wake up at 5:30 in the morning, determined to go over the tricky set theory proofs which looked like hieroglyphics to you the day before. There’s a test over the material later in the week and, with an already packed schedule, it’s imperative that you master this as quickly as possible.

Coffee brewed, you crack open the textbook and begin to go over the proofs. As usual it takes a quarter of an hour for the caffeine and the context to saturate your brain. By the time the first rays of morning lance through the twilight you’ve settled into time-worn scholarly rhythms.

But you’re rediscovering, to your consternation, that studying math rarely produces insights in linear time. After days of fruitless concentration insight could drop from the sky like a nuclear bomb, and there’s no guarantee that two concepts of roughly-equivalent difficulty will require a roughly-equivalent amount of time to grasp. Worse, there doesn’t even seem to be a clear process you can fall back on to force understanding. At least with history you can just slow down, take copious notes, and be reasonably confident that the bigger picture will fade into view.

Not so with set theory. You’ve already come to a step which you simply cannot make sense out of. With your intuitions spinning their tires in the mud of a topic they didn’t evolve to handle, you post a question to math.stackexchange and try desperately to understand the replies. Alas, even several rounds of follow-up questions don’t resolve the problem.

Now you’re just sort of…staring at the proof, chanting it to yourself like a litany against ignorance. You keep going back to the start, working through the first couple of steps that make sense, re-reading the preceding section for clues, reading ahead a little bit for yet more clues, and so on. Perhaps you try stackexchange again, or watch related videos on Youtube.

After ninety minutes of this you take a break and reflect back on the morning’s work. Not only do you not understand the set theory proofs, you’re not even sure what to type into Google to find the next step. If a friend were to ask you point blank what you’ve been doing, you’d struggle to formulate a reply.

And yet…some of the words do seem less arcane, and the structure of the proof feels more familiar somehow, like a building you pass on your way to work everyday but have never really stopped to look at. You have this nagging feeling that something-like-insight is hovering just out of your mind’s peripheral vision. You finish this study session with a vague, indefinable sense that progress has been made.

I call this frustrating state ‘semignosis'[1], and have spent a lot of time in it over the course of the STEMpunk Project. Once I had this term I realized there were a lot of interesting ideas I could generate by attaching different prefixes to ‘gnosis’, and thus I developed the following taxonomy:

Agnosis, n. — Simply not gnowing ( 😉 ) something.

Semignosis, n. — The state described above, where the seeds of future gnosis are being sown but there is no current, specifiable increase in gnowledge.

Infragnosis, n. — Gnowledge which you didn’t know you had; the experience of being asked a random question and surprising yourself by giving an impromptu ten-minute lecture in reply.

Gnosis, n. — Gnowing something, be it a procedure or a fact.

Misgnosis, n. — “Gnowing” something which turns out not to be true.

Supergnosis, n. — Suddenly grokking a concept, i.e. having an insight. Comes in a ‘local’ flavor (having an insight new to you) or a ‘global’ flavor (having an insight no one has ever had before).

Now that I’m sitting here fleshing out this idea, I realize that there are a few other possibilities:

Misinfragnosis, n. — Gnowledge you don’t gnow you had, but which (alas) ends up being untrue.

Gnostic phantom, n. — A false shape which jumps out at you because of the way an argument is framed or pieces are arranged; the mental equivalent of a Kanisza figure.

This is mostly just for fun. We already have a word for ‘insight’ so the word ‘supergnosis’ is superfluous (although it does sound like ‘supernova’, so maybe I could use the neologism in a story to make a character sound clever.) I doubt any of these terms will be used outside of this blog post.

But I think the term ‘semignosis’ is genuinely important. It captures a real state through which we must pass in our efforts to learn, and a very frustrating one at that. Having the term potentially allows us to do two things:

We can recognize the state as real and necessary, perhaps alleviating some of the distress felt while occupying it.

We can begin to classify fields by the amount of time a student of average intelligence must spend in semignosis.

We can start to think more clearly about how to approach and navigate this state.

The second point is one I want to expand upon in the not-too-distant future, and the thirds is one I’m continually grappling with; there’ll probably be a section devoted to it in the STEMpunk book.

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5 thoughts on “A Taxonomy of Gnoses”

Hey, I just stumbled upon your blog and wanted to say the STEMpunk Project is awesome. I really like what you’ve been doing and I’ll be following your progress keenly. I’ve been doing something similar of my own; I’m teaching myself computer science, programming, and mathematics. Let’s see how it goes.

The state of semignosis is quite irritating to me. I often think about its roots, and I’m starting to think that it’s because I’ve got my ego wrapped around the idea that I can just “get” an idea or concept after listening a lecture or following a (text)book. Being challenged in university for the first time has definitely pushed me to come to terms with this.

Haha, indeed it is! A lot of bright people aren’t really challenged until they get to university and discover they have to, y’know, actually *work* : ) If you make the investment, though, you’ll wind up much better off than you would otherwise have been.